Finite Group Databasebeta

← C131×#33738 #45719622

Subgroups — C131×#33738 #45719622

Order 33536.

510 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3170×C131C211yesmaximal, characteristic, complemented
2#3168×C131C211yesmaximal, characteristic
3#2255×C131C211yesmaximal, characteristic, complemented
4#2251×C131C211yesmaximal, characteristic, complemented
5#2245×C131C211yesmaximal, characteristic, complemented
6#2243×C131C211yesmaximal, characteristic, complemented
7#2220×C131C212yesmaximal
8#2219×C131C212yesmaximal, complemented
9C4×Q32×C131C212yesmaximal, complemented
10C4×SD32×C131C212yesmaximal, complemented
11C4×M32×C131C211yesmaximal, characteristic, complemented
12#533×C131—21no—
13#529×C131—21no—
14C2×Q32×C131C2212yes—
15C2×SD32×C131C2212yes—
16C2×M32×C131C2212yes—
17#500×C131C2211yescharacteristic
18#499×C131C2211yescharacteristic
19#495×C131C2211yescharacteristic
20#494×C131C2211yescharacteristic
21#488×C131—21no—
22#487×C131—21no—
23#467×C131—21no—
24#467×C131C2211yescharacteristic
25#467×C131C2212yes—
26#466×C131C2211yescharacteristic
27#465×C131—21no—
28C4×Q16×C131—21no—
29C4×Q16×C131C2211yescharacteristic
30C4×Q16×C131C2212yes—
31C4×SD16×C131—21no—
32C4×D8×C131C2211yescharacteristic
33C2×C4×C8×C131C2211yescharacteristic
34#367×C131C2212yes—
35#366×C131C2212yes—
36#358×C131C2212yes—
37#358×C131C2212yes—
38#358×C131C2212yes—
39#357×C131C2212yes—
40#346×C131C2211yescharacteristic
41#346×C131C2211yescharacteristic
42C4×C16×C131C2212yes—
43C2×Q16×C131—21no—
44C2×Q16×C131C2312yes—
45C2×Q16×C131C2311yescharacteristic
46C2×SD16×C131—21no—
47C2×D8×C131C2311yescharacteristic
48C22×C8×C131D411yescharacteristic
49C22×C8×C131C2311yescharacteristic
50C4⋊Q8×C131—21no—
51C4⋊Q8×C131—21no—
52#126×C131—41no—
53#125×C131—21no—
54#125×C131—41no—
55#124×C131—21no—
56#123×C131—41no—
57C22⋊Q8×C131—21no—
58C22⋊Q8×C131—22no—
59C22⋊Q8×C131—41no—
60#121×C131—21no—
61C4×Q8×C131—21no—
62C4×Q8×C131—22no—
63C4×Q8×C131—41no—
64C4×D4×C131—21no—
65C4×D4×C131—41no—
66#117×C131—41no—
67#117×C131—41no—
68C2×C42×C131D411yescharacteristic
69Q32×C131—24no—
70SD32×C131—24no—
71M32×C131—24no—
72C2×C16×C131C2312yes—
73C2×C16×C131C2312yes—
74#107×C131—21no—
75#107×C131C2311yescharacteristic
76#107×C131C2311yescharacteristic
77#107×C131C2312yes—
78#106×C131—21no—
79#103×C131—21no—
80#103×C131—22no—
81#103×C131—21no—
82#103×C131—22no—
83#102×C131—21no—
84#102×C131—21no—
85C4×C8×C131D411yescharacteristic
86C4×C8×C131D411yescharacteristic
87C4×C8×C131C2311yescharacteristic
88C4×C8×C131C2311yescharacteristic
89C2×Q8×C131—21no—
90C2×Q8×C131—22no—
91C2×Q8×C131—41no—
92C2×D4×C131—21no—
93C2×D4×C131—41no—
94C22×C4×C131—41no—
95C22×C4×C131D811yescharacteristic
96C22×C4×C131D811yescharacteristic
97C22×C4×C131C2×D411yescharacteristic
98Q16×C131—22no—
99Q16×C131—22no—
100Q16×C131—22no—
101Q16×C131—42no—
102SD16×C131—42no—
103D8×C131—22no—
104C2×C8×C131—22no—
105C2×C8×C131—22no—
106C2×C8×C131C2×D411yescharacteristic
107C2×C8×C131C2×D411yescharacteristic
108C2×C8×C131C2×D411yescharacteristic
109C2×C8×C131C2411yescharacteristic
110C4⋊C4×C131—21no—
111C4⋊C4×C131—21no—
112C4⋊C4×C131—22no—
113C4⋊C4×C131—41no—
114C4⋊C4×C131—41no—
115C4⋊C4×C131—41no—
116C4⋊C4×C131—41no—
117C4⋊C4×C131—41no—
118C4⋊C4×C131—42no—
119C4⋊C4×C131—41no—
120C4⋊C4×C131—42no—
121C4⋊C4×C131—41no—
122C22⋊C4×C131—42no—
123C22⋊C4×C131—41no—
124C22⋊C4×C131—41no—
125C22⋊C4×C131—41no—
126C22⋊C4×C131—41no—
127C22⋊C4×C131—41no—
128C42×C131—41no—
129C42×C131—42no—
130C42×C131D811yescharacteristic
131C42×C131D811yescharacteristic
132C42×C131C2×D411yescharacteristic
133C42×C131C2×D411yescharacteristic
134C16×C131—22no—
135C16×C131#4114yes—
136C23×C131—41no—
137C23×C131C2×D811yescharacteristic
138Q8×C131—42no—
139Q8×C131—41no—
140Q8×C131—41no—
141Q8×C131—42no—
142Q8×C131—82no—
143D4×C131—41no—
144D4×C131—41no—
145D4×C131—82no—
146C2×C4×C131—21no—
147C2×C4×C131—21no—
148C2×C4×C131—22no—
149C2×C4×C131—41no—
150C2×C4×C131—41no—
151C2×C4×C131—41no—
152C2×C4×C131—42no—
153C2×C4×C131—42no—
154C2×C4×C131—41no—
155C2×C4×C131—82no—
156C2×C4×C131C2×D811yescharacteristic
157C2×C4×C131C2×D811yescharacteristic
158C2×C4×C131C2×D811yescharacteristic
159C2×C4×C131C2×D811yescharacteristic
160C2×C4×C131C2×D811yescharacteristic
161C2×C4×C131C22×D411yescharacteristic
162C8×C131—21no—
163C8×C131—21no—
164C8×C131#13512yes—
165C8×C131C2×#4112yes—
166C22×C131—21no—
167C22×C131—21no—
168C22×C131—21no—
169C22×C131—81no—
170C22×C131—81no—
171C22×C131—81no—
172C22×C131C22×D811yescharacteristic
173C4×C131—21no—
174C4×C131—21no—
175C4×C131—21no—
176C4×C131—21no—
177C4×C131—81no—
178C4×C131—81no—
179C4×C131—82no—
180C4×C131—81no—
181C4×C131—82no—
182C4×C131#51012yes—
183C4×C131#53211yescharacteristic
184C4×C131C2×#13511yescharacteristic
185C2×C131—41no—
186C2×C131—161no—
187C2×C131#316911yescharacteristic
188C2×C131C2×#51011yescharacteristic
189C2×C131#341411yescharacteristic
190#33738C13111yesmaximal, characteristic, direct product factor, Sylow
191C131#3373811yescharacteristic, direct product factor, Sylow
192#3170C2×C13111yescharacteristic, complemented
193#3168C2×C13111yescharacteristic
194#2255C2×C13111yescharacteristic, complemented
195#2251C2×C13111yescharacteristic, complemented
196#2245C2×C13111yescharacteristic, complemented
197#2243C2×C13111yescharacteristic, complemented
198#2220C2×C13112yes—
199#2219C2×C13112yescomplemented
200C4×Q32C2×C13112yescomplemented
201C4×SD32C2×C13112yescomplemented
202C4×M32C2×C13111yescharacteristic, complemented
203#533—21no—
204#529—21no—
205C2×Q32C22×C13112yes—
206C2×SD32C22×C13112yes—
207C2×M32C22×C13112yes—
208#500C22×C13111yescharacteristic
209#499C22×C13111yescharacteristic
210#495C22×C13111yescharacteristic
211#494C22×C13111yescharacteristic
212#488—21no—
213#487—21no—
214#467—21no—
215#467C22×C13111yescharacteristic
216#467C22×C13112yes—
217#466C22×C13111yescharacteristic
218#465—21no—
219C4×Q16—21no—
220C4×Q16C22×C13111yescharacteristic
221C4×Q16C22×C13112yes—
222C4×SD16—21no—
223C4×D8C22×C13111yescharacteristic
224C2×C4×C8C22×C13111yescharacteristic
225#367C22×C13112yes—
226#366C22×C13112yes—
227#358C22×C13112yes—
228#358C22×C13112yes—
229#358C22×C13112yes—
230#357C22×C13112yes—
231#346C22×C13111yescharacteristic
232#346C22×C13111yescharacteristic
233C4×C16C22×C13112yes—
234C2×Q16—21no—
235C2×Q16C23×C13112yes—
236C2×Q16C23×C13111yescharacteristic
237C2×SD16—21no—
238C2×D8C23×C13111yescharacteristic
239C22×C8D4×C13111yescharacteristic
240C22×C8C23×C13111yescharacteristic
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243#126—41no—
244#125—21no—
245#125—41no—
246#124—21no—
247#123—41no—
248C22⋊Q8—21no—
249C22⋊Q8—22no—
250C22⋊Q8—41no—
251#121—21no—
252C4×Q8—21no—
253C4×Q8—22no—
254C4×Q8—41no—
255C4×D4—21no—
256C4×D4—41no—
257#117—41no—
258#117—41no—
259C2×C42D4×C13111yescharacteristic
260Q32—24no—
261SD32—24no—
262M32—24no—
263C2×C16C23×C13112yes—
264C2×C16C23×C13112yes—
265#107—21no—
266#107C23×C13112yes—
267#107C23×C13111yescharacteristic
268#107C23×C13111yescharacteristic
269#106—21no—
270#103—21no—
271#103—22no—
272#103—21no—
273#103—22no—
274#102—21no—
275#102—21no—
276C4×C8D4×C13111yescharacteristic
277C4×C8D4×C13111yescharacteristic
278C4×C8C23×C13111yescharacteristic
279C4×C8C23×C13111yescharacteristic
280C2×Q8—21no—
281C2×Q8—22no—
282C2×Q8—41no—
283C2×D4—21no—
284C2×D4—41no—
285C22×C4—41no—
286C22×C4D8×C13111yescharacteristic
287C22×C4D8×C13111yescharacteristic
288C22×C4C2×D4×C13111yescharacteristic
289Q16—22no—
290Q16—22no—
291Q16—22no—
292Q16—42no—
293SD16—42no—
294D8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8C2×D4×C13111yescharacteristic
298C2×C8C2×D4×C13111yescharacteristic
299C2×C8C2×D4×C13111yescharacteristic
300C2×C8C24×C13111yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—42no—
310C4⋊C4—41no—
311C4⋊C4—42no—
312C4⋊C4—41no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C42—41no—
320C42—42no—
321C42D8×C13111yescharacteristic
322C42D8×C13111yescharacteristic
323C42C2×D4×C13111yescharacteristic
324C42C2×D4×C13111yescharacteristic
325C16—22no—
326C16#41×C13114yes—
327C23—41no—
328C23C2×D8×C13111yescharacteristic
329Q8—42no—
330Q8—41no—
331Q8—41no—
332Q8—42no—
333Q8—82no—
334D4—41no—
335D4—41no—
336D4—82no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—82no—
347C2×C4C2×D8×C13111yescharacteristic
348C2×C4C2×D8×C13111yescharacteristic
349C2×C4C2×D8×C13111yescharacteristic
350C2×C4C2×D8×C13111yescharacteristic
351C2×C4C2×D8×C13111yescharacteristic
352C2×C4C22×D4×C13111yescharacteristic
353C8—21no—
354C8—21no—
355C8#135×C13112yes—
356C8C2×#41×C13112yes—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22C22×D8×C13111yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—81no—
369C4—81no—
370C4—82no—
371C4—81no—
372C4—82no—
373C4#510×C13112yes—
374C4#532×C13111yescharacteristic
375C4C2×#135×C13111yescharacteristic
376C2—41no—
377C2—161no—
378C2#3169×C13111yescharacteristic
379C2C2×#510×C13111yescharacteristic
380C2#3414×C13111yescharacteristic
subgroupG/H
centerC2×C4×C131C2×D8
commutator, Frattini, cosocleC2×C8C24×C131
socleC22×C131C22×D8
prime radical#466×C131C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C131 ◁ C2×C42×C131 ◁ C2×C4×C8×C131 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3170×C131C2semidirect
3. #2255×C131C2semidirect
4. #2251×C131C2semidirect
5. #2245×C131C2semidirect
6. #2243×C131C2semidirect
8. #2219×C131C2semidirect
9. C4×Q32×C131C2semidirect
10. C4×SD32×C131C2semidirect
11. C4×M32×C131C2semidirect
190. #33738C131direct (N × H)
191. C131#33738direct (N × H)
192. #3170C2×C131semidirect
194. #2255C2×C131semidirect
195. #2251C2×C131semidirect
196. #2245C2×C131semidirect
197. #2243C2×C131semidirect
199. #2219C2×C131semidirect
200. C4×Q32C2×C131semidirect
201. C4×SD32C2×C131semidirect
202. C4×M32C2×C131semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#3170×C1312
#3168×C1312
#2255×C1312
#2251×C1312
#2245×C1312
#2243×C1312
#2220×C1312
#2219×C1312
C4×Q32×C1312
C4×SD32×C1312
C4×M32×C1312
#33738131